A statement identified the accused as Carlo Alberto Capella and said he was arrested earlier on Saturday in the Vatican after a warrant was issued by the Holy See's chief magistrate at the end of an investigation.
The Vatican statement said Capella, who was recalled from the Vatican embassy in Washington last August, was arrested according to articles of a 2013 law signed by Pope Francis. The articles cited by the statement related to child pornography.
If indicted, the monsignor will have to stand trial in the Vatican and faces up to 12 years in jail.
The scandal is the latest blow to the Catholic Church as it struggles to overcome repeated sex abuse cases among its clergy.
Francis has declared zero tolerance over abuse scandals that have beset the Church for decades, but critics say he has not done enough, particularly to hold bishops responsible for mishandling or covering up abuse.